tickets sold

Question

University theater sold 556 tickets for a play. Tickets cost $22 per adult and $12 per senior citizen. If total receipts were $8492, how many senior citizen tickets were sold?

Answer 1

Lauren,

This is a system of equations problem.  What you are looking for are two equations in this word problem.  The first equation is the easy equation most of the time which involves the quantity of tickets.  Meaning 556 tickets sold to the variables of A(adult) and S(senior citizen).  These are my variables and you can name them whatever you want.  It's easier for me to answer the question related to the adult or senior citizen.  The idea here is the first equation is A + S = 556.

The second equation is based on the amount of money being collected.  We attach the values of each ticket to the type of ticket sold, either an adult ticket or senior citizen ticket.  So, the second equation is 22A + 12S = 8492.  The 8492 is the total number of dollars collected for the sale of the tickets.  There are your two equations that you have to solve for and I'm gonna let you do that part.  Good luck in your class the rest of the way.  If you ever need a tutor, join Wyzant!  There are thousands of tutors available to help you.

Answer 2

s = number of senior tickets at $12 each

556 - s = number of adult tickets at $22 each

 

12s + 22(556 - s) = 8492

 

-10s = -3740

 

s = 374

 

Test the answer.